Question 4

We find the angles by dividing a full circle by how many times the figure looks the same.

Step 1 — Finding the First Angle

A figure has rotational symmetry. It looks the same after we turn it. We turn it around a central point. The smallest turn makes it look the same. This is the angle of rotational symmetry.

Look at our figure. It has 3 identical parts. They are like spokes of a wheel. We can turn it. One spoke moves to the next spoke's spot. A full circle is 360 degrees. There are 3 identical parts. So, we divide 360 degrees by 3.

$360^\circ \div 3$

$\boxed{120^\circ}$

Step 2 — Finding Other Angles

We found the first angle is 120 degrees. If we turn it again by 120 degrees, it looks the same. So, we add 120 degrees to the first angle.

$120^\circ + 120^\circ$

$\boxed{240^\circ}$

If we turn it one more time by 120 degrees, it completes a full circle. So, we add 120 degrees to the second angle.

$240^\circ + 120^\circ$

$\boxed{360^\circ}$

Every figure looks the same after a 360 degree turn.

Answer

(i) The first angle of rotation is 120 degrees. (ii) The second angle of rotation is 240 degrees. (iii) The third angle of rotation is 360 degrees.